Solutions Homework 2
Name: ___________________________________ Date:_____________ Period: _______________
1. Where on the normal curve are the inflection points located?
Where the slope starts to drop off at.
2. What is the standard normal distribution?
A standard Normal distribution is a Normal curve with a mean of 0 and a standard deviation of 1.
3. What information does the standard normal table give?
The area that falls to the left of the given z-score.
4. How do you use the standard normal table (Table A) to find the area under the standard normal curve to the left of a given z-value? Draw a sketch.
Locate the z-score to the nearest 10th along the left hand side, then follow it to the right to find the hundredth and look at the corresponding proportion.
5. How do you use Table A to find the area under the standard normal curve to the right of a given z-value? Draw a sketch.
Subtract the proportion you find from 1.
6. How do you use Table A to find the area under the standard normal curve between two given z-values? Draw a sketch.
Find the z-scores for both given values of x. Find the proportions in Table A. Subtract the smaller proportion from the larger on.
10. Below are two normal curves, both with mean 0. Approximately what is the standard deviation of each curve?
For the narrow one, about 0.3. For the shorter one, about 0.6.
11. The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes, then mark the horizontal axis.)
12. The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions.
a) What percent of men are taller than 74 inches?
b) Between what heights do the middle 95% of men fall?
c) What
1. Where on the normal curve are the inflection points located?
Where the slope starts to drop off at.
2. What is the standard normal distribution?
A standard Normal distribution is a Normal curve with a mean of 0 and a standard deviation of 1.
3. What information does the standard normal table give?
The area that falls to the left of the given z-score.
4. How do you use the standard normal table (Table A) to find the area under the standard normal curve to the left of a given z-value? Draw a sketch.
Locate the z-score to the nearest 10th along the left hand side, then follow it to the right to find the hundredth and look at the corresponding proportion.
5. How do you use Table A to find the area under the standard normal curve to the right of a given z-value? Draw a sketch.
Subtract the proportion you find from 1.
6. How do you use Table A to find the area under the standard normal curve between two given z-values? Draw a sketch.
Find the z-scores for both given values of x. Find the proportions in Table A. Subtract the smaller proportion from the larger on.
10. Below are two normal curves, both with mean 0. Approximately what is the standard deviation of each curve?
For the narrow one, about 0.3. For the shorter one, about 0.6.
11. The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes, then mark the horizontal axis.)
12. The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions.
a) What percent of men are taller than 74 inches?
b) Between what heights do the middle 95% of men fall?
c) What